Graphical Calculation Method for Minimum Reflux Ratio in Azeotropic Distillation'

GRAPHICAL CALCULATION METHOD FOR MINIMUM REFLUX RATIO IN AZEOTROPIC DISTILLATION'

SHOZO TANAKA AND JIRO YAMADA** Shin-etsu Chemical Industry Co., Ltd., Tokyo, Japan

In an azeotropic distillation column, the rate of net flow and the composition of net flow for both stripping and rectifying sections can be calculated from the limiting conditions of the separation desired. The pinch points are dotted on the radial lines starting from the point of net flow composition by trial and error, and locus of the pinch points are traced on the triangular diagram by the way of connecting the pinch points. Each minimum reflux ratio of stripping and rectifying sections can be calculated from the quan- titative ratio of vapor and liquid of the operating line passing the point of intersection of locus line and feed line, and the larger of the two values shall be defined as the minimum reflux ratio of the system. For example, we illustrate the graphical calculation method for AcOH-H2O-BuOAc system and AcOH-H2O-EtOAc system.

Jm^Vm-Lm+i=~W, ^mi=Xwi DXdi-SXSf Introduction An-Vn+i Lin-L) b, Oni- D-S Recently, some substantial papers on calculation [II] when the entrainer is supplied with the feed to method for azeotropic distillation have been reported the column, by Yorizane et al.6>7\ Yamada et al.5\ and Hirose Jm=-W, et alAK The authors previously proposed a graph- ^ni~Xdi ical calculation method of minimumreflux ratio of (4) the azeotropic distillation, and in this paper we report The minimum reflux ratio in the stripping section some results of additional study. is obtained from Eq.(5) in either case [I] or [II] The graphical method is suitable for the calculation ^min D -1 of non-ideal system distillation such as azeotropic (5) distillation, since we can reasonably use a complicated The minimumreflux ratio in the rectifying section vapor-liquid equilibrium on a diagram by this is calculated from Eq.(6) and Eq.(7). method. This graphical method sometimes may give an approximate result for the distillation, as the case [I] r'mla=_^(D ^L_S_ (6) vapor-liquid equilibrium is expressed by a diagram case [II] r"min=P" (7) geometrically, but this method is considered to be Comparing with rmin and r'min or rmin and r"mln, practical if the vapor-liquid equilibrium curve is accurate. obtained from the previous equation, the larger value The operating line is given by Eq.(l) and Eq.(2) is selected as the minimumreflux ratio of that azeo- on the triangular diagram. The net flow rate J tropic distillation. The ratio of flow rate p is determined on the triangular diagram in the way shown and its composition d are shown by Eq.(3) or Eq.(4), in the previous paper. the selection of which maydepend on the entrainer supplying position, On the other hand, in our previous paper, we deter- stripping section : mined the flow rate ratio p' or p" in the rectifying VmYmi-Lm+jX(m+iji IJm\dn section on the condition that Yn+1and Xn approach (i) the composition of the distillate gradually, where p' rectifying section : or p" is shown by Eq.(8) Vn+iY(n+1)i -LnXni+Jn8n[ (2) (or P")= L [I] when the entrainer is supplied to the top of the An(8) ^-n ^n+1 column, In this paper we tried to obtain p' or p"from the operating line passing through a point of pinch composition on the feed line in a manner mentioned Received on October 26, 1970 Presented at the 7th symposiummeeting of the Soc. of later. We should explain how to determine the Chem. Engrs., Japan, at Tokyo, November 1968 locus of a pinch point in the column under a given Unitika Chemical Co., Ltd. separating condition of an azeotropic distillation 20 :2o: JOURNAL OF CHEMICAL ENGINEERING OF JAPAN Yn+1dB Ac O H Xw

,¥¥^ y2 Fig. 1 Procedure to reach thepinch point. Example, AcOH-H2O-BuOAc system V , ¥ 2L ,

Bu oA c H2O

X w

x ,

X ,

x 3 r>

A 2¥ Fig. 2 Procedure to reach thepinch point. Example, AcOH-H2O-EtOAc system 'A

a t O A c H ,0 as a result of studying in series with the previous paper. Weillustrate with an example in which the 1. A Trial and ErrorMethod for the Locus of the locus has a tendency to approach the point of net Pinch-Point flow composition or the azeotropic composition. Moreover, we discuss the concentration of acetic acid We explain a main point to get the pinch-locus in aqueous solution by azeotropic distillation, operat- of stripping section for the azeotropic distillation of ing with reflux ratio larger or smaller than the mini- acetic acid aqueous solution on the triangular diagram mumreflux ratio calculated by the method in this by a trial and error method. Drawing a straight paper, for reference with the graphical calculation line Xwafor the 1st step from the net flow composi- method. Werefer to the influence on the operation tion of stripping section Xwito the azeotropic com- of a difference in the entrainer. position ai on Fig. 1 and Fig. 2, one plots the vapor

VOL. 972 5 NO. ;2i; 21 composition^! being in equilibrium with Xi, which is an intersection with the supplying line, for instance. The pinch-composition of stripping section is defined as a point where a line XwXjYj becomes just straight, located in an area separated by XwXxAiand includ- ing XiYi. In the same manner the next optional point X2 is set on the supplying line and the plotted Y2 being in equilibrium with X2. X2Y2, unexpect- edly, has an opposite inclination to XiY1? so Xj orYj, Rur-4 xui which makes XwXjXj a straight line, should come between Xi and X2 or Yt and Y2. The pinchpoint Xu X3 or Y3 is provided easily by the above-mentioned Rl trial and error method. The locus of pinch-point has IM ^ M a tendency to concentrate around the net flow com- n position andthe azeotropic composition,so weshould I ^ H ^ ^ H be able to obtain it very easily, even if only a few n*1 I ^ H ^ ^ ^ points of pinch composition are discovered. AcOH HｻC n 2. The Azeotropic Distillation Using Butyl Acetate as m tl I ^ H ^ ^ ^ Entrainer m Steam For the azeotropic distillation of acetic acid aqueous solution, if acetic acid is comparatively dilute, butyl acetate can be used as an entrainer that is heavier Stea m than the bottom product, and is fed to the top of the X w column. In this ternary system, the phenomenon is Hi.0- 10 P I utilized that butyl acetate and water maymake a X w AcOH ~ 1.0 minimumboiling point azeotrope, (butyl acetate 27.8 mol%, water 72.2 mol% and its boiling point Fig. 3 Azeotropic distillation apparatus for AcOH-H2O- is 91°C). Wequoted Hirata's2) vapor-liquid equilib- BuOAc system rium data. We supposed conveniently that the entrainer is not separated into two layers and distilled out or returned for reflux just as a condensing com-

AcO H Cl- Omi =Xwi

¥ N .

¥ ¥S ¥ ¥¥ Yrni I ¥ M y IXJ Locus of pinch point (liq.) in strip- Iy, pingLocussectionof pinch point (vap.) in Xni v¥ ¥vA stripping section IIX, Locustifyingofsectionpinch point (liq.) in rec- IIy, Locusof pinch point (vap.) in rectifying section / * s Fig. 4 Locus of pinch points for AcOH- B u O A C H , 0 H2O-BuOAc system

22 (22) JOURNALOF CHEMICALENGINEERINGOF JAPAN position, and that entrainer is newly supplied to the A cO H top of the column. That is a reasonable assumption for calculation for reasons mentioned later. The azeotropic distillation equipment of this system is u composed of two columns, and a condenser and a two-layer separator are used in commonbetween column I and II. In the entrainer-recovery equipment column II, the waste product is regarded as ¥ s^ almost pure water, so the distillate of column I has V the same significance as the waste of column II in ¥ the ordinary state. (Fig. 3) L ¥ Therefore, it is not necessary to consider the effect ¥ of solubility change of butyl acetate to the water phase by liquid temperature. But controlling the ¥ reflux of column I in the operation, we should consider the effect of the mutual solubility of an individual I ./ component. That.is, in Eq.(9), it is necessary to control the outward reflux of every phase (right side) to make the summation of the flow rate of every component into the column equal to the theoretical value (left side). / , * 13 SLEXK1+st=2RuXut+2RlXl1 v^ (9) A . P In Fig. 4, when the net flow composition of the B u O A C H 2 O stripping section dmi is equal to (XwAcoh4= 1.0 Xwh2o ^Xwbuoac^fO) and that of the rectifying section dni I l l D i s t il l a t i o n c ur v e u n d e r t o t a l r e f lu x is equal to (X3nH2o4=1.0, X^acoh^X^buoac^O), a Fig. 5 Distillation curve under total reflux for AcOH-H2O- locus of pinch-point is drawn by the previous men- BuOAc system tioned method. Ix and Iy are the liquid-phase line and the vapor-phase line of pinch-locus of the stripping section, respectively, and it seems to approach the azeotropic composition. IIX or IIy is similarly the pinch-locus of the rectifying section. The curve III in Fig. 5 is the distillation line of total reflux, calcu- c A.O 15 lated by drawing for acetic acid-water binary system c Va p i o a d to the 4th theoretical plate, and there adding butyl iJ V m (m in acetate by an amount of0.01. Ten theoretical plates o were required as a result of the ternary drawing. or X The operating line at a finite reflux ratio (r>rmin) ZJ 1 . 0 1 1 passes an area surrounded by Ix and III in the o> _ 1 "O 2.0 ov- -｣^ stripping section and enters the rectifying section, and CL *. the operating region lies at the side locating the y: fmir / fmin 5 r azeotropic point against the curve IIX. If the pinch 0.5 10 > ' point is supposed to be near the feed plate, Xmi ｫw ｻ that is a point of intersection of the pinch liquid- phase line and ike supplying line, and Ymi being in equilibrium with Xmi. In the same manner, the I pinch composition of rectifying section is located on 0 0.5 the diagram. From these pinch compositions, p or XfA c O H (mol p' on the triangular diagram can be determined and rmin and r'mln is obtained by Eq.(5) and Eq.(6), Fig. 6 Correlation to Xf and rmin,, r'min.# Vm(min), and by employing p, the vapor load corresponding AcOH-H2O-BuOAc system to rmin is calculated from Eq.(10). p= vn section should be located near the feed plate. Fig. . v m w (10) 7 shows the case where the operating reflux ratio r These relations, based on the condition F=1.0 mol/ is smaller than rmin in the stripping section. When time, are indicated in Fig. 6 and rmin>r/min is obvious Xmi comes near the pinch point on XfS, the liquid from this. The separation of the azeotropic distil- composition would scarcely change and could not lation under fixed conditions is possible if a finite operate the desirable separation howevermuchthe reflux ratio is selected on the basis of rmin obtained theoretical plates are increased. Fig. 8 is a case on the assumption that the pinch point of the stripping where r>rmin. The binary system AcOH-H2O VOL. 5 NO 1 1972 .^3> 23 is drawnto the 5th theoretical plate, and there butyl 蝣蝣 acetate in an amountof 0.01 is addedand drawing AcOH on the triangular diagramis continued.Nowwe V s.- 蝣蝣 explain the drawingmethodon the diagram. Link- ing Y15, being in equilibrium with X15, to dmi by a 6 straight line, and putting X16 dividing line Yl5£mi

10 to the ratio of p with Eq.(10), X17 is located in the samemanner.X17 came to the rectifying section over the line XfS, so the operating line should be k changed for that of the rectifying section, and obtaining Yi7 in equilibrium with Xn, a line dniY17 should 15 be extrapolated by Eq.(8) to the ratio p' to decide the location of X18. Obtaining Yi8, being in equilibrium with X18,and drawingshould be continued and repeatedin the samemanner.In this exercise, the liquid (XfAcoH=0.3) is fed and operating at 20 * I reflux r=1.0 (>rmin=0.42) under the separating t condition of XwAcOh>0.99 and XdAcOH<0.01. 20 I ^ ^ ^ H Pinch Point theoretical plates are required by the graphical calculation method. I 3. The Azeotropic Distillation with Ethyl Acetate for I I I I I f I n I an Entrainer 蝣蝣 For an entrainer, whenacetic acid is comparatively BuOAc H20 concentrated, ethyl acetate would be suitable. It is lighter than the bottomproduct andis fed to the r=0.3¥x y,5 rectifying section, the operating region is a downward < 18,K t*y, area of curve IIX. Curve IV is regarded as the distillation curve at total reflux, whenwater is v20 y,r Cs^ On," used for the entrainer, but it is not examined in A .PuoAc detail adequately. In Fig.9 using Xmi or Xni B obtainedby the samemanneras explainedin section 2, if /5 or p" could be determined onthe diagram, XfAcOH=0.3 r orx" should be obtained by Eq.(5) and Eq.(7). r== 1.0>rmin. =0.42 Fig. ll showsthe mutual relations amongrmin5r"min Fig. 8 Case of r>rmin in AcOH-H2O-BuOAc system and Vm(min)for the feed composition XfAc0H- In this systemthe minimumreflux ratio at the stripping

24 [24] JOURNALOF CHEMICALENGINEERINGOF JAPAN A cO H X . o mi- A mi �J ¥ ^K 4 0 3 .0 ¥ ¥ ¥ X V a p L o a d I I M ^ B m J ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ E ^ H ¥ xf dor 3 D jr X i ( m in ) D 2 . 5 a / ¥ o I ¥ / _ J u_ 2. 0 o L ¥ X ni 2C a . f a 2 . 0 > ' 1.0 rm in S S , V fcn i X m¥i y ｫ 1.5 ¥Iｻ ¥¥¥ I 0 0. 5 X . A c O H ( m oL t ra c t. )

Fig. ll Correlation to Xf and rmln., r'min., Vm(min), in - iJs AcOH-H2O-EtOAc system s / E t A c AZPEOBITN TR O P I C H 2C

I Locus of pinch point (liq.) in stripping section A c O H I (vap .) O m i IIx, Locus of pinch poit (liq.) in rectifying section I (vap .) 5 Fig. 9 Locus of pinch point in AcOH-H2O-EtOAc system

AcO H

3 t^ x , 4 1 / ¥ 10 1 ¥

it ¥ pinch Point

¥B av ¥ ¥ I I I I I I I I I I ¥ L E t o A c H 2O ¥ I V ¥ X fAfiO H = 0 .5 I r= 0. 4 5 r"min. Fig. 12 is a A. P case where r (real operating reflux ratio) is smaller than rmin, and Fig. 13 indicates the case of r>rmin. Et O A c H 2O This example is calculated with the ternary diagram adding EtOAcfor an amount of0.01 at 5th theoretical Ill Distillation curve under total reflux plate, after drawing the AcOH-H2O binary system Fig. 10 Distillation curve under total reflux in AcOH-H2O- by McCabe-Thiele's method. In this problem, EtOAc system a feed mixture with XfAcoH=0.5 is fed to the column 25 VOL. 5 NO.972 1 25; plained with respect to both acetic acid~water-^ A c O H butyl acetate ternary system and acetic acid~water~ ethyl acetate ternary system for the example. 5 Acknowledgement We are grateful to Managing Director M. Nakagawa, and collaborator H. Araki (Shinetsu Chemical Co., Ltd.).

Nomenclature D = rate of overhead product [mol/time] X , F = rate offeed [mol/time] L = flow rate of liquid in column [mol/time] R = rate of reflux flowing out of decanter [mol/time] r = reflux ratio in stripping section r' = reflux ratio in rectifying section for case (I) (defined by Eq.(6)) r"= reflux ratio in rectifying section for case (II) 1 (defined by Eq.(7)) Pmch-poi'nt S = rate of entrainer [mol/time] V = flow rate of vapor in column [mol/time] W=rate of bottom product [mol/time] x = composition of liquid phase [mol fraction] 14 y = composition of vapor phase [mol fraction] A.P J = rate of net flow [mol/time] E O A c H 20 d = composition of net flow [mol fraction] p = flow ratio instrippingsection \ (definedz/m by m )/ XfAc0H= ;0.5 pf = flow ratio in rectifying section for case (I) r= 1.3>rmln. =0.6.5. (defined by -^-) Fig. 13 Case of r>rmin. in AcOH-H2O-EtOAc system p"= flow ratio in rectifying section for case (II) (defined by -^-) and distilled under the operating condition of r=1.3 ^Subscripts) (>rmin=0.65). 14 theoretical plates would be neces- d = overheadproduct sary to do the separation being XwAcoh>0.99 and f = feed i = individual component XdAcoH<0-01with our graphical calculation method. L = lowerlayerin decanter m= number of plate in stripping section Conclusion min = minimum n = numberof plate in rectifying section In azeotropic distillation, the net flow rate and R =reflux its composition in the stripping section and the U = upper layer in decanter rectifying section are calculated on the basis of the W= bottomproduct stated conditions of fractionation. On the radial straight lines starting from the point of the net flow Literature Cited composition at the triangular vapor-liquid equilibrium diagram, the pinch points are plotted by the 1) Ellis, S., et al.: Brit., Chem. Engr., 2, 648 (1957) 2) Hirata, M. and Y. Hirose: Kagaku Kdgaku, 30, 121 trial and error method, and the line of the pinch locus (1966) is drawn on the diagram. The individual minimum 3) Hirose, Y. and H. Hiraiwa: Kagaku Kdgaku 32, 998 reflux ratio of the stripping section or the rectifying (1968) section can be determined from the ratio of quantities 4) Tanaka, S. and J. Yamada: Kagaku Kdgaku, 29, 118 of vapor and liquid at the intersection point of a (1965) 5) Yamada, I., H. Sugie and K. Abe: Kagaku Kdgaku, 31, line of a pinch locus and the feedline. The larger 395 (1967) value calculated now should be selected for the 6) Yorizane, M. and S. Yoshimura: Kagaku Kdgaku, 29, real minimumreflux ratio of the appointed fractiona- 229 (1965) 7) Yorizane, M. and S. Yoshimura: Kagaku Kdgaku, 32, tion. Still more the operating region could be inferred 382 (1968) from the distillation line at total reflux and the locus of the pinch-point. The graphical solution is ex-

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